You are attending a loud concert. To avoid ear damage, you decide to move father from the stage. Sound intensity is given by the formula I= k/d2, where k is the constant and d is the distance in meters form the listener to the source of the sound. Determine the expression for the decrease in sound intensity if you move x meters farther from the stage?
To determine the expression for the decrease in sound intensity if you move x meters farther from the stage, we need to compare the initial sound intensity (I1) at the original distance to the sound intensity (I2) at the new distance.
We know that sound intensity is given by the formula I = k/d^2, where I is the sound intensity, k is the constant, and d is the distance in meters from the listener to the source of the sound.
Let's denote the initial distance as d1 and the new distance as d2.
The initial sound intensity (I1) at the original distance (d1) can be represented as:
I1 = k / d1^2
Now, when you move x meters farther from the stage, the new distance becomes (d1 + x). Therefore, the sound intensity (I2) at the new distance (d2) can be represented as:
I2 = k / (d1 + x)^2
To find the decrease in sound intensity, we need to calculate the difference between the initial and new sound intensities:
Decrease in sound intensity = I1 - I2
Substituting the values of I1 and I2 into the equation, we have:
Decrease in sound intensity = (k / d1^2) - (k / (d1 + x)^2)
Simplifying the expression further may require additional information, such as the specific values of k, d1, and x.